1
ENEE 222 Signals and Systems
Fall 2011 –Test 1 – 2011

09

28

Solutions
All problems count the same 25 points
Problem 1:
(a 12.5 points) Given the matrix
[
]
, find vectors
v,w
so that
v
T
Aw= f.
(b 12.5 points) How many floating point operations does it take to compute
A
2
?
Solution:
(a) Choose
[
]
, in the product
Aw
this picks off the last column of
A.
Choose
[
]
, in the product
v
T
Aw
this picks off the second element of
Aw
, which is
f.
(b) To obtain the
“
11
”
element of
A
2
we multiply the first column of
A
by the first row of
A
and
sum the products. This requires 3 multiplications and 2 additions. Repeating this to compute each
of the 9 elements in
A
2
we need 27 multiplies and 18 adds, a total of 45 floating point operations.
Problem 2:
Let
G
be an
m
2 matrix and let
u,v
be defined by
[
] [
]
.
(a 5 points) What are the dimensions of
u,v
? (b 20 points) Express
[
]
in terms of
u
and
v.
Solution:
(a) The vectors are both
m
1. (b) Let
g
1
and
g
2
be the columns of the matrix
G,
then the
first expression gives 
g
1
+
g
2
=
u
and the second gives 2
g
1
+
g
2
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '13
 Simon
 Addition, Multiplication, difference equation, floating point operations

Click to edit the document details